QCD with overlap fermions: Running coupling and the 3-loop beta-function

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QCD with overlap fermions: Running coupling and the 3-loop beta-functionWe calculate the relation between the bare coupling constant g 0 and the MSbar-renormalized coupling g MS: g 0 = Z gg 0,a \mu g MS, to 2 loops in perturbation theory. We employ the standard Wilson action for gluons and the overlap action for fermions. For convenience, we have worked with the background field technique, which only requires evaluation of 2-point Greens function for the problem at hand. Our results depend explicitly on the number of fermion flavors N f and colors N. Since the dependence of Z g on the overlap parameter rho cannot be extracted analytically, we tabulate our results for different values in the allowed range of rho 0 rho 2, focusing on values which are being used most frequently in simulations. Knowledge of Z g allows us to derive the 3-loop coefficient of the bare beta-function beta Lg 0 which, unlike the 1- and 2-loop coefficients, is regularization-dependent. The nontrivial dependence of Z g and of beta Lg 0 on rho is plotted for various choices of N, N f.